Nonfattening condition for the generalized evolution by mean curvature and applications

Nonfattening condition for the generalized evolution by mean curvature and applications

We prove a non fattening condition for a geometric evolution described by the level set approach. This condition is close to those of Soner \cite{soner93} and Barles, Soner and Souganidis \cite{bss93} but we apply it to some unbounded hypersurfaces. It allows us to prove uniqueness for the mean curv...

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Veröffentlicht in:Interfaces and free boundaries 2008-01, Vol.10 (1), p.1-4
Hauptverfasser: Biton, Samuel, Cardaliaguet, Pierre, Ley, Olivier
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Biology and other natural sciences
Fluid mechanics
Mathematics
Numerical analysis
Optimization and Control
Partial differential equations
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Cardaliaguet, Pierre
Ley, Olivier
description We prove a non fattening condition for a geometric evolution described by the level set approach. This condition is close to those of Soner \cite{soner93} and Barles, Soner and Souganidis \cite{bss93} but we apply it to some unbounded hypersurfaces. It allows us to prove uniqueness for the mean curvature equation for graphs with convex at infinity initial data, without any restriction on its growth at infinity, by seeing the evolution of the graph of a solution as a geometric motion.
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subjects Biology and other natural sciences
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Mathematics
Numerical analysis
Optimization and Control
Partial differential equations
title Nonfattening condition for the generalized evolution by mean curvature and applications
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